The present invention relates to nanometerology and in particular to calibration methods, calibration standards, and calibration systems for nano-scale measuring devices.
Nano-scale measuring devices, which include electron microscopes and scanning probe microscopes (SPMs), are devices capable of making measurements with a spatial resolution of 10 nm or less. The ability to resolve small differences means that these devices are very precise. A nano-scale measuring device may be able to measure, when comparing objects, differences in feature size on the order of nanometers, or even Angstroms. Yet a very precise measurement is not necessarily an accurate one. Accuracy refers to the correctness of a measurement in absolute terms.
To obtain measurements that are accurate as well as precise, calibration of the measuring device is generally required. Calibration usually involves measurements made on samples having known dimensions or otherwise well characterized. Calibration is intended to ascertains systematic errors so that they may be taken into account in interpreting device measurements Calibration measurements are subsequently used to correct measurement data to remove or mitigate systematic errors.
The sources of systematic error and the number of measurements required to calibrate a device depend on the type of device. Consider an atomic force microscope (AFM) 200 (a type of SPM), illustrated in FIG. 1a. The atomic force microscope 200 measures the topography of a sample 210. A controller 220 directs a sample stage 230 to move the sample 210 past a detection tip 240, which is mounted on a cantilever 250. As the sample 210 moves past the detection tip 240, the sample stage 230 provides the controller 220 with feedback regarding the position of the sample stage 230 and an interferometer 260 provides the controller 220 with data regarding the height of the cantilever 250. The controller 220 combines the sample position data, the tip position data, and data regarding the tip shape to reconstruct the sample topography.
Each source of data to the controller 220 may contain systematic error. With respect to the sample position data, for example, the feedback provided by the sample stage 230 may be the number or turns in a screw that controls the position of the sample stage 230. Relating the number of turns in the screw to the actual position of the sample may introduce systematic error. With respect to tip movement data, the readings from the interferometer 260 may not have a one-to-one correspondence with the actual movement of the detection tip 240. For example, the point 252 on the cantilever 250 on which the interferometer 260 is focused moves at a different rate than the detection tip 240 if the point 252 is a different distance from the cantilever pivot point 254. Finally, because the movement of the detection tip 240 depends on the shape of the detection tip 240 as well as the topography of the sample 230, errors in data regarding the shape of the detection tip 240 lead to errors in the topography data produced by the AFM 200.
An ideal calibration of a nano-scale measuring device, one that would take into account all sources of systematic error regardless of their source, would involve making measurements on a series of calibration standards with precisely known shapes and sizes spanning the range of shapes and sizes of objects to which the instrument is to be applied. The accuracy with which the dimensions of the standards are known is ideally greater than the precision of the device being calibrated, an order of magnitude greater if possible. For nano-scale measuring devices, obtaining standards having the ideal precision and range of shapes and sizes has proven difficult, if not impossible. Available standards are not characterized with the desired degree of accuracy and are not suitable for addressing all sources of systematic error.
For example, Bartha et al., U.S. Pat. No. 5,665,905 (the xe2x80x9cBartha patentxe2x80x9d) provides a calibration standard for calibrating the shape of a SPM tip. The standard has a trench and a raised line, the trench having a width intended to be equal to the thickness of the line. The widths of the trench and raised line are about 500 nm and the uncertainty of these widths is at least about +/xe2x88x921 nm due to the roughness of the surfaces. The SPM is calibrated by moving the calibration standard past the SPM detection tip. The measured width is based on the SPM measurements and the movements of the sample stage.
First the SPM scans a trench. Prior to entering the trench, the SPM measures a first height value, the height outside the trench. As the scanning tip enters the trench, the SPM measurement undergoes a first transition after which the SPM measures a second height, the height at the base of the trench. As the scanning tip leaves the trench, the SPM measurement undergoes a second transition as the SPM returns to measuring the first height. The measured width of the trench is considered to be the length over which the sample stage, or SPM tip, moves from the beginning of the first transition to the end of the second transition. It is expected that this measured width is less than the actual width of the trench due to the finite tip width. The first transition does not begin until a trailing portion of the tip enters the trench. The second transition begins as soon as the leading portion of the tip leaves the trench. Therefore, the measured width of the trench is approximately the actual width of the trench minus the tip width.
To complete the calibration, the raised line is scanned. As the scanning tip reaches the line, the SPM measurement undergoes a third transition as the SPM goes from measuring a third height to a fourth height. As the scanning tip passes the line the SPM measurement undergoes a fourth transitions in which the SPM returns to measuring the third height. The measured width of the line is considered to be the length over which the sample stage, or the SPM tip, moves from the beginning of the third transition to the end of the fourth transition. It is expected that this measured width is greater than the actual width of the line due to the finite tip width. The third transition begin when the leading portion of the tip reached the line. The fourth transition ends when the trailing portion of the tip passes the line. Therefore, the measured width is approximately the actual line width plus the tip width.
The two measurements may be combined to calibrate the tip width. Assuming that the actual line and trench widths are equal, the measure width of the line is approximately two tip widths greater than the measured width of the trench. The tip width is calculated by taking the difference between these two measurements and dividing by two. Applying the calibration consists of adding the calculated tip width to measured trench widths and subtracting the calculated tip width from measured line widths.
A number of factors limit the accuracy of this calibration. For example, there is the uncertainty in the line and trench widths. The calibration provides only one number, the tip width, but the tip shape may be relatively complex. Other potential sources of systematic error not taken into account include: inaccuracy in the stage or SPM tip movement measurements, differences between the line and trench widths, and difficulty in identifying the exact starts and ends of the height measurement transitions.
Another SPM calibration standard and calibration method is provided by Bayer et al., U.S. Pat. No. 5,578,745 (the xe2x80x9cBayer patentxe2x80x9d). The Bayer patent calibration standard is formed by making several sharp groves in a single crystal material. The groves have well defined slopes that meet to form relatively sharp peaks. The peak radii are measured with a scanning electron microscope (SEM) or transmission electron microscopy (TEM) and are said to be known within +/xe2x88x920.5 nm. SPM tip widths are calibrated by scanning across the peaks of the calibration standard. The radius of the curve measured by scanning across a peak less the peak radius is taken to be the SPM tip width. The sources of error in this calibration method, which include uncertainty in the peak radii (+/xe2x88x920.5 nm) and over-simplification of the peak and SPM tip shape, are similar to the sources of error affecting the Bartha patent method.
The Bayer patent method improves over the Bartha patent by providing the possibility of partially calibrating measurements of X (distance across the sample) and measurements of Z (height of the sample). The Bayer patent provides calibration standards with deep groves having relatively well defined length to width ratios. These calibration standards may be used to calibrate the ratio between X displacement and Z displacement measurements, which is referred to as the xe2x80x9cZ-linearityxe2x80x9d of the SPM. If the X measurements are thought to be known accurately, this method may be used to calibrate displacements of the SPM tip in the Z-direction.
Firstein et al., U.S. Pat. No. 5,585,211 (the xe2x80x9cFirstein patent) provides a grating of approximately equal sized lines and spaces for calibrating SEMs. The calibration relies on the accuracy of the grating period. The grating is formed using electron beam lithography with beam placement controlled by laser-based interferometry. The grating is relatively coarse and the uncertainty in its pitch is several nanometers. Thus the Firstein patent calibration standard is not very precise and has a limited range of applicability.
There remains an unsatisfied need for calibration standards having accurately known dimensions, for more accurate methods of calibrating nano-scale measuring devices, and for nano-scale measuring systems that provide more accurate measurements.
The present invention provides systems, methods, and standards for calibrating nano-measuring devices. Calibration standards of the invention include carbon nanotubes and methods of the invention involve scanning carbon nanotubes using nano-scale measuring devices. The widths of the carbon nanotube calibration standards are known with a high degree of accuracy. The invention allows calibration of a wide variety of nano-scale measuring devices, taking into account many, and in some cases all, of the systematic errors that may affect a nano-scale measurement. The invention may be used to accurately calibrate line width, line height, and trench width measurements and may be used to precisely characterize both scanning probe microscope tips and electron microscope beams.
One aspect of the invention provides a calibration standard for a nano-scale measuring device including a carbon nanotube and a substrate, wherein the carbon nanotube is adherent to the substrate.
Another aspect of the invention provides a reference standard for a nano-scale measuring device including a carbon nanotube and means for securing the carbon nanotube in a position suitable for making a calibration scan of the carbon nanotube using the nano-scale measuring device.
A further aspect of the invention provides a package having contents including a carbon nanotube and instructions for using the contents as a reference standard for a nano-scale measuring device.
A further aspect of the invention provides a method of making a calibration standard for a nano-scale measuring device including adhering a carbon nanotube to a substrate.
A further aspect of the invention provides a nano-scale measuring system including a nano-scale measuring device, a calibration standard comprising a carbon nanotube, and a controller, wherein the controller is adapted to calibrate the nano-scale measuring device using a measurement of the calibration standard made with the nano-scale measuring device.
A further aspect of the invention provides a method of calibrating a nano-scale measuring device including scanning a section of a carbon nanotube with a nano-scale measuring device to obtain scan data and calibrating the nano-scale measuring device using the scan data.
To the accomplishment of the foregoing and related ends, the invention comprises the features hereinafter fully described and particularly pointed out in the claims. The following description and the annexed drawings set forth in detail certain illustrative aspects and implementations of the invention. These are indicative, however, of but a few of the various ways in which the principles of the invention may be employed. Other objects, advantages and novel features of the invention will become apparent from the following detailed description of the invention when considered in conjunction with the drawings.